Are the Data and the Fit Holographic?

One has to ask if the data is holographic, that is, does it fit a single curve and follow a single rule? This would allow us not only to extrapolate the fit beyond the existing data but also to make predictions about the future. As with optical holograms, a part of the hologram contains information about the entire image. As a result, the fit may be useful outside the range of magnitudes for which there is data. We may be able to see "over the horizon" but the curve for the data would have to be continuous with no jumps in it.

One of the problems with the fit that was obtained is that the deviations of the histogram points from the fit curve are greater than expected. Near the peak they are way beyond the 3σ bounds. This indicates that the fluctuations are probably not statistical in nature. One has to consider the possibility that there is some correlation among events in the occurrance of earthquakes. We can no longer assume that they are statistically independent events. Among the possibilities are a common cause, aftershocks following a major earthquake or an earthquake at one location may stimulate earthquakes elsewhere. Is there an earthquake equivalent of a laser? If so, we should probably be more concerned about our neighbors.

One item that I forgot to mention is that the peak for the fit is at M 1.086. I also need to add a correction or maybe just a clarification concerning the failure of the "equilibrium distribution." The assumption that the distribution we were looking for was connected with the equilibrium distribution of the mechanism failed. Each mechanism and its transition matrix has an equilibrium solution. We can't exclude mechanisms just because they have equilibrium solutions. It is more likely that the simple feedback mechanism considered failed to give a distribution of the correct shape with a peak near M 1.1*.

*edit: It was possible to find a g function which produced a peak for an earthquake distribution but it was not where g = 1 which was a contradiction with the initial assumptions.